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IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC)

Density evolution thresholds for noise-against-noise min-sum decoders

Franklin Cochachin, David Declercq, Emmanuel Boutillon, Lounis Kessal

Published Oct 1, 2017• 7 citations
Publisher

Abstract

In this paper, we define Noise-against-Noise Min-Sum (NAN-MS) decoders as decoders that incorporate a certain amount of random perturbation due to deliberate noise injection. We introduce a noise model which is used to implement quantized NAN-MS decoders, using a limited number of precision bits. The behavior of NAN-MS decoders is investigated in the asymptotic limit of the code length using a noisy version of density evolution (DE). We use the noisy-DE thresholds to analyze and optimize the noise model parameters. We show that a controlled injection of noise allows NAN-MS decoders to achieve better performance than noiseless MS decoders, especially for low precision. The finite-length simulations confirm the conclusions of the DE analysis.

DOI
10.1109/pimrc.2017.8292326

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In this paper, we define Noise-against-Noise Min-Sum (NAN-MS) decoders as decoders that incorporate a certain amount of random perturbation due to deliberate noise injection. We introduce a noise model which is used to implement quantized NAN-MS decoders, using a limited number of precision bits. The behavior of NAN-MS decoders is investigated in the asymptotic limit of the code length using a noisy version of density evolution (DE). We use the noisy-DE thresholds to analyze and optimize the noise model parameters. We show that a controlled injection of noise allows NAN-MS decoders to achieve better performance than noiseless MS decoders, especially for low precision. The finite-length simulations confirm the conclusions of the DE analysis.
The novelty of this paper is to propose a new LDPC decoder called Sign-Preserving Noise-Aided Min-Sum (SP-NA-MS) decoder that improves the decoding performance compared to classical Offset Min-Sum (OMS) decoder when messages are quantized, with only 3 or 4 bits. The particularity of the SP-NA-MS decoder is that the variable-to-check messages are never set to 0, and always carry the sign information. Moreover, the decoder incorporates random perturbation due to deliberate noise injection. The parameters of the SP-NA-MS decoders are optimized in the asymptotic limit of the code length thanks to the Density Evolution (DE) method. The finite-length simulations confirm the conclusions of the DE analysis and gain of up to 0.3 dB in SNR can be obtained compared to regular OMS with same quantization level.
This paper investigates the behavior of the Min-Sum decoder running on noisy devices. Our aim is to evaluate the robustness of the decoder to computation noise caused by the faulty logic in the processing units. This type of noise represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the finite-precision min-sum decoder and then carry out the density evolution analysis of the noisy min-sum decoder. We show that, in some particular cases, the noise introduced by the device can help the min-sum decoder to escape from fixed points attractors and may actually result in an increased correction capacity with respect to the noiseless decoder. We also point out a specific threshold phenomenon, referred to as functional threshold, which accurately describes the convergence behavior of noisy decoders. The behavior of the noisy MS is demonstrated in the asymptotic limit of the code length through a noisy version of density evolution and is also verified in the finite-length case by Monte Carlo simulations.
This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.
This paper considers low-density parity-check (LDPC) decoders affected by deviations introduced by the electronic device on which the decoder is implemented. Noisy density evolution (DE) that allows to theoretically study the performance of these LDPC decoders can only consider symmetric deviation models due to the all-zero codeword assumption. A novel DE method is proposed that admits the use of asymmetric deviation models, thus widening the range of faulty implementations that can be analyzed. DE equations are provided for three noisy decoders: belief propagation, Gallager B, and quantized min-sum (MS). Simulation results confirm that the proposed DE accurately predicts the performance of LDPC decoders with asymmetric deviations. Furthermore, asymmetric versions of the Gallager B and MS decoders are proposed to compensate the effect of asymmetric deviations. The parameters of these decoders are then optimized using the proposed DE, leading to better ensemble thresholds and improved finite-length performance in the presence of asymmetric deviations.
This paper investigates the behavior of the noisy Min-Sum decoder over binary symmetric channels. A noisy decoder is a decoder running on a noisy device, which may introduce errors during the decoding process. We show that in some particular cases, the noise introduce by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length, by using “noisy” density evolution equations, and it is also verified in the finite-length case by Monte-Carlo simulation.
Motivated by the problem of designing fault-tolerant memories built out from unreliable components, this paper investigates the performance of two noisy Min-Sum-based decoders on Binary Symmetric Channels. We analyze the performance of the noisy Min-Sum decoder in terms of useful regions and target bit-error rate threshold values, derived by using “noisy” density evolution equations. We also present the finite length performance of two Min-Sum based decoders, and point out the excellent performance of the noisy Self-Corrected Min-Sum decoder, which exhibits almost the same performance as the noiseless decoder.